Kinetic and Mechanistic Aspects of Oxidation of Aminotriazole Formamidine by Cerium(IV) in Aqueous Perchloric and Sulfuric Acid Solutions: A Comparative Study

Article abstract of DOI:10.1007/s10953-016-0438-1

The kinetics of the oxidation of an aminotriazole formamidine derivative, N,N-dimethyl-N′-(4H-1,2,4-triazol-3-yl) formamidine (ATF) by cerium(IV) has been studied spectrophotometrically in aqueous perchloric and sulfuric acid solutions at constant ionic strength of 1.0 mol·dm^-3. In both acids, the reaction shows first order kinetics with respect to [Ce(IV)], whereas the orders with respect to [ATF] are less than unity. The reaction exhibits negative fractional order kinetics with respect to [H⁺]. The rates of reaction are not significantly affected by variations of either ionic strength or relative permittivity of the reaction's media. Addition of cerium(III) product does not affect the rates. Plausible mechanistic schemes for the reactions have been proposed. In both cases, the final oxidation products were identified as aminotriazole, dimethyl amine and carbon dioxide. Under comparable experimental conditions, the oxidation rate in perchloric acid solution is about sixfold higher than that in sulfuric acid solution. The effect of temperature on the rates has also been studied and activation parameters have been evaluated and discussed. The rate laws associated with the reaction mechanisms are derived.

Full text of DOI:10.1007/s10953-016-0438-1

J Solution Chem
DOI 10.1007/s10953-016-0438-1
Kinetic and Mechanistic Aspects of Oxidation
of Aminotriazole Formamidine by Cerium(IV)
in Aqueous Perchloric and Sulfuric Acid Solutions:
A Comparative Study
Ahmed Fawzy1,2
Received: 1 August 2015 / Accepted: 11 November 2015
Ó Springer Science+Business Media New York 2016
Abstract The kinetics of the oxidation of an aminotriazole formamidine derivative, N,N-
dimethyl-N0-(4H-1,2,4-triazol-3-yl) formamidine (ATF) by cerium(IV) has been studied
spectrophotometrically in aqueous perchloric and sulfuric acid solutions at constant ionic
strength of 1.0 molÁdm-3. In both acids, the reaction shows first order kinetics with respect
to [Ce(IV)], whereas the orders with respect to [ATF] are less than unity. The reaction
exhibits negative fractional order kinetics with respect to [H?]. The rates of reaction are
not significantly affected by variations of either ionic strength or relative permittivity of the
reaction’s media. Addition of cerium(III) product does not affect the rates. Plausible
mechanistic schemes for the reactions have been proposed. In both cases, the final oxi-
dation products were identified as aminotriazole, dimethyl amine and carbon dioxide.
Under comparable experimental conditions, the oxidation rate in perchloric acid solution is
about sixfold higher than that in sulfuric acid solution. The effect of temperature on the
rates has also been studied and activation parameters have been evaluated and discussed.
The rate laws associated with the reaction mechanisms are derived.
Keywords Kinetics Á Mechanism Á Oxidation Á Aminotriazole formamidine Á Cerium(IV)
1 Introduction
Cerium(IV) is a powerful one electron oxidizing agent especially in acid media [1–16].
The oxidizing potentialities of cerium(IV) in sulfuric acid medium have conclusively been
established [1–9]. Nevertheless, few reports on cerium(IV) oxidation in perchloric acid
&
1
Ahmed Fawzy
afsaad13@yahoo.com
Chemistry Department, Faculty of Applied Sciences, Umm Al-Qura University, Mecca, Saudi
Arabia
2
ˆ
Chemistry Department, Faculty of Science, Assiut University, Asyut, Egypt
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J Solution Chem
CH3
N
CH3
CH3
R'
R
N
N
N
N
Cl
N
Ar
CH3
N
N
N
H
CH3
(ATF)
(I)
(II)
(III)
Scheme 1 Structures of some substituted formamidines
media are available [10–15], probably due to presence of dimers and polymers of cer-
ium(IV) in such media [15]. However, the reactions of cerium(IV) in perchloric acid
proceed much faster than those in sulfuric acid. Cerium(IV) oxidations of various sub-
strates are found to follow different mechanisms, depending upon the acid medium used.
Generally, for oxidations by cerium(IV), it is interesting to understand the different
pathways of the reactions and different active forms of cerium(IV).
Tri-substituted formamidines of the general structure(I), shown in Scheme 1, have
achieved importance in the last few decades due to their very broad spectrum of biological
activity. The biochemical potentials of formamidines include monoamine oxidase inhibi-
tors [17, 18], and adrenergic and neurochemical receptors [19, 20]. The N,N-dialkyl
derivatives are highly effective acaricides and the most rewarding of these studies resulted
in discovery of the acaricide insecticide chlordimeform, structure(II) in Scheme 1. The
oxidative cleavage of formamidines is quite important, since the N,N-dialkyl formamidine
group is one of the most versatile protecting groups, especially in biosynthetic applications.
A literature survey reveals that no work has been reported about the kinetics and
mechanism of oxidation of aminotriazole formamidines by any oxidant. This observation
prompted this investigation into the kinetics and mechanism of oxidation of one substituted
aminotriazole formamidines, N,N-dimethyl-N0-(4H-1,2,4-triazol-3-yl) formamidine (ATF),
Scheme 1, by cerium(IV) in both perchloric and sulfuric acid solutions. The objectives of
the investigation are to establish optimum conditions affecting oxidation of ATF, to
understand the active species of the oxidant and reductant in such solutions, to check the
reactivity of ATF towards Ce(IV) in acid solutions and finally to elucidate plausible
reaction mechanisms.
2 Experimental
2.1 Materials
The aminotriazole formamidine derivative (ATF) was synthesized and identified as
reported elsewhere [21]. The stock solution of cerium(IV) was prepared by dissolving ceric
ammonium sulfate in 1.0 molÁdm-3 H2SO4, diluted with double distilled water and kept
overnight. The concentration of cerium(IV) was ascertained by titrating against standard
ferrous ammonium sulfate solution using ferroin as an internal indicator. The solution of
cerium(IV) was stored in a dark glass bottle and was used after 24 h, since the hydrolysis is
negligible after 12 h from preparation [22]. Cerium(III) solution was prepared by dis-
solving cerium(III) acetate in water. Sodium perchlorate and sodium sulfate were used to
vary the ionic strength in perchloric and sulfuric acid solutions, respectively. Other
123

J Solution Chem
chemicals employed in the present work were of reagent grade and their solutions were
prepared by dissolving the requisite amounts of the samples in doubly distilled water.
2.2 Kinetic Measurements
All kinetic runs were followed under pseudo-first order conditions with ATF in a large
excess over that of cerium(IV). The progress of the reactions was followed by monitoring
the decrease in absorbance of cerium(IV) as a function of time at k = 316 nm, its
absorption maximum, whereas the other constituents of the reaction mixtures do not absorb
significantly at this wavelength. The applicability of Beer’s law for cerium(IV) at 316 nm
has been verified, giving e = 4362 26 dm3Ámol-1Ácm-1 in agreement with earlier
reports [11, 12]. The absorbance measurements were made in a thermostatted quartz cell of
a path length of 1 cm, on a Shimadzu UV–VIS–NIR-3600 double-beam spectropho-
tometer. First order plots of ln (absorbance) versus time were found to be good straight
lines and the observed first order rate constant values (kobs) were calculated as the gradients
of these plots. The rate constants were reproducible to within 4 % and are the average of at
least three independent kinetic runs. The reaction orders (n) with respect to the reactants in
both acid solutions were determined from the slopes of log10 kobs versus log10 (C) plots by
varying the concentrations (C) of substrate and acids, in turn, while keeping other con-
ditions constant. The in situ H? concentration in sulfuric acid–sulfate medium was cal-
culated by using known ionization constant [23]. In the case of perchloric acid solutions,
[H?] was maintained by adding requisite concentration of HClO4 by subtracting the [H?]
added due to H2SO4 present in cerium(IV) stock solution.
3 Results
3.1 Stoichiometry and Product Identification
Different sets of reaction mixtures containing various amounts of Ce(IV) and ATF at fixed
acidity, ionic strength and temperature were allowed to react for 24 h in closed vessels for
completion of reactions. The unreacted [Ce(IV)] was assayed spectrophotometrically at
316 nm as well as by titrating against standard ferrous ammonium sulfate solution. The
results obtained in both media indicated that two moles of Ce(IV) are consumed by one
mole of ATF to yield the oxidation products as shown in Scheme 2:
N
N
N
N
N
N
OH
H
+ 2Ce(III) + 2H+
+ 2Ce(IV) + H2O
=
(1)
(2)
NMe2
NMe2
N
NMe2
N
H
N
N
H
(I)
(II)
N
N
OH
CO2 + HNMe2
+
+ H2O
=
N
N
H
N
H
NH2
(II)
(III)
(IV)
Scheme 2 Stoichiometric equations for the oxidation of ATF by Ce(IV) in acid solutions
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J Solution Chem
where the compounds (I), (II), (III) and (IV) are ATF, 1,1-dimethyl-2-hydroxy-3-(4H-
1,2,4-triazol-3-yl) formamidine as an intermediate product, aminotriazole and dimethy-
lamine, respectively. The above stoichiometric equations are consistent with the results of
product identification as described elsewhere [21]. Aminotriazole and dimethyl amine were
identified by liquid chromatography and spot tests [24], respectively, and carbon dioxide
by lime water.
3.2 Spectral Changes
The spectral changes for the oxidation of aminotriazole formamidine by cerium(IV) in both
perchloric and sulfuric acid solutions are shown in Fig. 1a, b, respectively. In both cases,
the scanned spectra show a gradual disappearance of the Ce(IV) band at its absorption
maximum with time as a result of its reduction to Ce(III). It can be observed that the decay
of Ce(IV) during the oxidation reaction carried out in perchloric acid solution is signifi-
cantly faster than that in sulfuric acid solution.
3.3 Effect of [Ce(IV)]
The oxidant Ce(IV) was varied in both reactions in the range of (0.5–6.0) 9 10-4 molÁdm-3
keeping other variables constant. It has been observed that the increase in the oxidant
concentration does not alter the values of the rate constants (Table 1). Also, the plots of
ln (absorbance) versus time plots were found to be good straight lines. These results indicate
that the order of reactions with respect to the oxidant concentration is confirmed to be one.
3.4 Effect of [ATF]
The observed rate constants were determined at different initial concentrations of the
reductant ATF while other variables were kept constant. It was found that increasing [ATF]
increases the rates (Table 1). Plots of the observed rate constants versus [ATF] at constant
(a)
(b)
Fig. 1 Spectral changes during oxidation of ATF by Ce(IV) in: a perchloric acid, and b sulfuric acid
solutions: [ATF] = 6.0 9 10-3, [Ce(IV)] = 2.0 9 10-4, [H?] = 0.5 and I = 1.0 molÁdm-3 at 293.2 K;
scan time intervals are 1 min
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J Solution Chem
Table 1 Effect of [Ce(IV)], [ATF] and [H?] on kobs for the oxidation of ATF by Ce(IV) in perchloric and
sulfuric acid solutions at 293.2 K
104 [Ce(IV)] (molÁdm-3
)
103 [ATF] (molÁdm-3
)
[H?] (molÁdm-3
)
104 kobs (s-1
)
Perchloric
Sulfuric
0.5
1.0
2.0
3.0
4.0
5.0
6.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.3
0.4
0.5
0.6
0.7
0.8
28.8
29.3
29.0
29.7
28.7
27.9
29.4
16.2
19.4
24.3
29.0
32.5
37.1
40.9
46.1
39.9
34.2
29.0
24.9
21.5
18.5
4.7
5.1
4.9
4.8
4.9
4.7
4.9
2.8
3.5
4.1
4.9
5.5
6.4
7.3
9.6
7.5
5.8
4.9
4.2
3.7
3.4
Experimental error 4 %. I = 1.0 molÁdm-3
Fig. 2 Plots of kobs versus [ATF]
in the oxidation of ATF by
Ce(IV) in perchloric and sulfuric
acid solutions:
[Ce(IV)] = 2.0 9 10-4
[H?] = 0.5 and
,
I = 1.0 molÁdm-3 at 293.2 K
123

J Solution Chem
Fig. 3 Plots of log10 kobs versus
log10 [H?] for the oxidation of
ATF by Ce(IV) in perchloric and
sulfuric acid solutions:
[ATF] = 6.0 9 10-3
,
[Ce(IV)] = 2.0 9 10-4 and
I = 1.0 molÁdm-3 at 293.2 K
pH are linear with positive intercepts (Fig. 2), confirming the fractional order dependences
with respect to [ATF] for both the acids.
3.5 Effect of [H1]
Kinetic runs were carried out by varying the hydrogen ion concentration (0.2–0.8 molÁdm-3
)
with perchloric acid and sulfuric acids and keeping the concentrations of all other reactants
constant. It was observed that the rates of the reaction decrease with increasing [H?] in both
acids (Table 1). Plots of kobs versus [H?] are linear with negative slopes (figure not shown)
confirming negative fractional-first order dependences with respect to [H?]. Furthermore, the
plots of log10 kobs versus log [H?] were linear with slopes of -0.66 and -0.87 in perchloric
and sulfuric acids, respectively, as shown in Fig. 3.
3.6 Effect of Ionic Strength and Relative Permittivity of the Acid Media
The effect of ionic strength on the rates of the reactions was studied by varying the ionic
strength in the range 1.0–2.2 molÁdm-3 using sodium perchlorate in the case of perchloric
acid and sodium sulfate in case of sulfuric acid while keeping the concentrations of all
other reactants constant. The results indicate that variation of ionic strength was found to
have negligible effect on the reaction rates in both cases.
The relative permittivity (e) effect was studied by varying the acetic acid–water content
in the reaction mixtures with all other conditions being kept constant. The relative per-
mittivities were computed from the values of pure liquids by considering their values e in
pure form using equation: e = e1V1 1 e2V2, where V1 and V2 are volume fractions and e1
and e2 are relative permittivities of water and acetic acid as 78.5 and 6.15 at 298.15 K,
respectively. The rate constants increased negligibly with decreasing relative permittivity
of the acid solutions.
3.7 Effect of [HSO24 ]
In the case of sulfuric acid, kinetic runs were carried out at different concentrations of
bisulfate in the range 0.3–0.9 molÁdm-3, keeping the concentrations of all other reactants
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J Solution Chem
Fig. 4 A plot of 1/kobs versus
[HSO-4 ] for the oxidation of ATF
by Ce(IV) in sulfuric acid
solution: [ATF] = 6.0 9 10-3
,
[Ce(IV)] = 2. 9 10-4
[H?] = 0.5 and
,
I = 1.0 molÁdm-3 at 293.2 K
constant. It was observed that increase in bisulfate concentration decreases the rate of the
reaction and the order with respect to [HSO-4 ] was negative. This is confirmed by the linear
plot of 1/kobs versus [HSO-4 ] with positive intercept as shown in Fig. 4.
3.8 Effect of Initially Added Product
The effect of added cerium(III) product was studied in the concentration range
0.5–6.0 9 10-4 molÁdm-3 at fixed concentrations of the oxidant, reductant and acids. It
was found that Ce(III) did not have any significant effect on the rates of reactions in either
perchloric or sulfuric acid solutions.
3.9 Effect of Temperature
The rates of the reactions were carried out at four different temperatures: 283, 293, 303 and
313 K, at constant concentrations of the reactants and other conditions being constant. The
results indicate that the pseudo-first order rate constants increase with increasing tem-
perature. The activation parameters of the second order rate constant (k0) were calculated
using Arrhenius, Fig. 5a, and Eyring, Fig. 5b, plots and are listed in Table 2.
3.10 Effect of Mn21 and Al31 Catalysts
In both perchloric and sulfuric acid solutions, the rates of the reactions were measured at
various [Mn2?] and [Al3?] (3.0–9.0 9 10-5 molÁdm-3) with other conditions being con-
stant. The results show that the rates increased with increase in both [Mn2?] and [Al3?] and
the catalytic efficiency of Al3? was higher than that of Mn2? as shown in Figs. 6 and 7.
3.11 Test for Free Radical Intermediates
It is well known [1–6, 9–11] that cerium(IV) is a generator of free radicals, due to its single
equivalent change in redox reactions. Hence, the intervention of free radicals during the
reactions was examined as follows. The reaction mixtures, to which known quantities of
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(a)
(b)
Fig. 5 a Arrhenius and, b Eyring plots in the oxidation of ATF by Ce(IV) in perchloric and sulfuric acid
solutions: [ATF] = 6.0 9 10-3, [Ce(IV)] = 2.0 9 10-4, [H?] = 0.5 and I = 1.0 molÁdm-3
Table 2 Activation parameters of the second order rate constants k’ for the oxidation of ATF by Ce(IV) in
perchloric and sulfuric acid solutions
Reaction
DS= (JÁmol-1ÁK-1
)
DH= (kJÁmol-1
)
DG=298 (kJÁmol-1
)
E=a (kJÁmol-1
)
Perchloric acid
Sulfuric acid
-194.54
-223.82
18.12
6.48
75.12
71.76
20.55
9.04
[ATF] = 6.0 9 10-3
error 3 %
,
[Ce(IV)] = 2.0 9 10-4
,
[H?] = 0.5 and I = 1.0 molÁdm-3
.
Experimental
Fig. 6 Effect of [Mn2?] and
[Al3?] on kobs in the oxidation of
ATF by Ce(IV) in perchloric acid
solution: [ATF] = 6.0 9 10-3
,
[Ce(IV)] = 2.0 9 10-4
[H?] = 0.5 and
,
I = 1.0 molÁdm-3 at 293.2 K
acrylonitrile scavenger have been added initially, were kept in inert atmosphere for 2 h.
Upon diluting the reaction mixtures with methanol, white precipitates formed, implying the
generation of free radicals in the reactions. When the experiments were repeated in the
absence of ATF under similar conditions, the tests were negative. This indicates that the
reactions were routed through free radical paths.
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Fig. 7 Effect of [Mn2?] and
[Al3?] on kobs in the oxidation of
ATF by Ce(IV) in sulfuric acid
solution: [ATF] = 6.0 9 10-3
,
[Ce(IV)] = 2.0 9 10-4
[H?] = 0.5 and
,
I = 1.0 molÁdm-3 at 293.2 K
4 Discussion
4.1 Kinetically Active Cerium(IV) Species in Acid Solutions
A survey on the earlier literature on the nature of cerium(IV) species in perchloric acid
solution [25–27] showed that the active species of cerium(IV) was found to be either free
monomeric species Ce4?, its hydrolyzed forms, Ce(OH)3? and Ce(OH)22?, or partially in
the form of dimeric species (Ce–O–Ce)6? and (HOCe–O–CeOH)4?. However, Offiner and
Skoog [28] showed from the spectrophotometric studies that the hydrated form, Ce4?, is
the predominant species at [H?] C 1.0 molÁdm-3 for Ce(IV) concentrations up to
1.5 9 10-3 molÁdm-3, whereas the hydrolyzed forms and dimers are predominant at
[H?] \ 0.8 molÁdm-3. Therefore, under our experimental conditions of low [H?] and
deceasing reaction rate with increasing [H?], Ce(OH)3? may be regarded as the kinetically
active form of cerium(IV) according to the following equilibria:
KOH
3þ
Ce4þ þ H2O ꢀ CeðOHÞ þ Hþ:
In sulfuric acid medium [1–9], and depending upon the concentrations of H?, HSO4-
and H2SO4, Ce(IV) forms several sulfate complexes such as Ce(SO4)2?, Ce(SO4)2,
HCe(SO4)-3 and HCe(SO4)-4 , although their role has not received much attention. Based on
the effects of [H?] and [HSO-4 ] on the rate of the reaction, one or other of these species
were treated to be the kinetically active species of cerium(IV). The following equilibria
[29] lead to the formation of sulfato complexes of cerium(IV):
K1
2þ
Ce4þ þ SO24À ꢀ CeðSO4Þ
K2
ðAÞ
CeSO24þ þ SO42À ꢀ Ce(SO4Þ2 ðBÞ
K3
CeðSO4Þ2 þ HSOÀ4 ꢀ HCeðSO4ÞÀ3 ðCÞ
K4
HCeðSO4ÞÀ3 þ HSO4À þ Hþ ꢀ HCeðSO4ÞÀ4 ðDÞ
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The observations that both H? and HSO4- ions retard the rate of oxidation point to the fact
that HCe(SO4)-3 (equilibrium D) may be considered as the kinetically active species, which
shows parallels with variations of kobs with both [H?] and [HSO4-] in the present inves-
tigation as shown in Figs. 3 and 4. As the sulfuric acid concentration increases both the
[H?] and [HSO-4 ] also increase. If the rate is inversely dependent on the [HSO-4 ] to a great
extent then the overall effect of adding sulfuric acid would lower the rate as obtained
experimentally (Table 1). Similar behavior has been reported elsewhere [29].
4.2 Reaction Mechanism
The reactions between ATF and Ce(IV) in both perchloric and sulfuric acid media have a
stoichiometry of 1:2, i.e., one mole of ATF requires two moles of Ce(IV). The reactions
exhibit first order dependence with respect to [Ce(IV)], less than unit orders with respect to
[ATF] and negative fractional orders in [H?]. The rate is not significantly affected by
Ce(III), ruling out the probability of any fast equilibrium with the product, preceding the
rate-determining step. The rate-determining step should be irreversible as is generally the
case for one electron oxidants [30] and the oxidation takes place through generation of free
radicals as found experimentally. The rates of reaction are not significantly affected by
variation of either ionic strength or relative permittivity of the reactions medium, sug-
gesting that the reactions occur between a neutral molecule and charged ions [31, 32].
The less than unit orders with respect to [ATF] presumably result from formation of
complexes between the different Ce(IV) species and ATF prior to the rate-determining
steps. Complexes formation was proved kinetically by the non-zero intercepts of the
plots of 1/kobs versus 1/[ATF] (Fig. 8) in favor of possible formation of an intermediate
complex between the oxidant and substrate, similar to the well-known Michaelis–
Menten [33] mechanism for enzyme–substrate reactions. The failure of the spec-
trophotometric detection of such intermediate complexes (Fig. 1) may be interpreted by
either lower concentrations of the reactants used and, hence, the expected lower
absorbitivities of the formed complexes and/or the fast subsequent decomposition of the
intermediates in comparison with their formation. The complexes formed were slowly
decomposed in the rate-determining steps to give rise to the initial oxidation products
as the substrate radical (ATFÁ) and Ce(III). The substrate radical reacts with another
Ce(IV) species in a subsequent fast step to yield an intermediate product, 1,1-dimethyl-
2-hydroxy-3-(4H-1,2,4-triazol-3-yl) formamidine (or 1,1-dimethyl-3-(4H-1,2,4-triazol-3-
yl) urea). In a further fast step, the intermediate product is hydrolyzed to give the final
oxidation products, as given in Schemes 3 and 4 for reactions in perchloric and sulfuric
acids, respectively. Since such Schemes are in accordance with the generally accepted
principle of non-complementary oxidations taking place in a sequence of one-electron
steps, the reaction between the substrate and oxidant would afford radical intermediates
as was observed.
4.2.1 Reaction Mechanism in Perchloric Acid Solution
Ce4þ þ H2O KꢀOH Ce(OH)3þ þ Hþ
ð3Þ
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J Solution Chem
N
N
N
N
H
H
K
+ Ce(OH)3+
(4)
(5)
(6)
(7)
(8)
(C1)
NMe2
Ce(OH)3+
N
NMe2
NMe2
N
H
N
N
H
N
N
N
N
H
.
+ Ce3+ + H2O
k1
slow
N
N
H
NMe2
N
N
H
Ce(OH)3+
N
N
N
N
OH
fast
.
+ Ce3+
+ Ce(OH)3+
NMe2
OH
N
NMe2
N
H
N
N
N
H
N
N
OH
N
N
fast
+ H2O
+
NMe2
fast
N
H
N
H
NH2
O
NMe2
OH
CO2 + HNMe2
O
NMe2
Scheme 3 Mechanism of oxidation of ATF by Ce(IV) in perchloric acid solution
The suggested mechanism leads to the following rate law (see Appendix 1),
k1KOHK½CeðIVފ½ATFŠ
Rate ¼
ð9Þ
ð10Þ
ð11Þ
½HþŠ þ KOH þ KOHK½ATFŠ
Under pseudo-first order condition, the rate-law can be expressed by Eq. 10,
Àd½CeðIVފ
Rate ¼
¼ kobs½Ce(IV)Š
dt
Comparing Eqs. 9 and 10, the following relationship is obtained,
k1KOHK½ATFŠ
kobs
¼
½HþŠ þ KOH þ KOHK½ATFŠ
The rate law (Eq. 9) is consistent with all the observed orders with respect to different
species, which can be verified by rearranging to the following equations:
ꢀ
ꢁ
1
½HþŠ þ KOH
1
1
¼
þ
ð12Þ
kobs
k1KOH
K
½ATFŠ k1
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J Solution Chem
Fig. 8 Plots of 1/kobs versus
1/[ATF] in the oxidation of ATF
by Ce(IV) in perchloric and
sulfuric acid solutions:
[Ce(IV)] = 2.0 9 10-4
[H?] = 0.5 and
,
I = 1.0 molÁdm-3 at 293.2 K
Fig. 9 Plots of 1/kobs versus
[H?] in the oxidation of ATF by
Ce(IV) in perchloric and sulfuric
acid solutions:
[ATF] = 6 9 10-3
,
[Ce(IV)] = 2.0 9 10-4 and
I = 1.0 molÁdm-3 at 20 293.2 K
ꢀ
ꢁ
1
¼
1
1
1
½HþŠ þ
þ
ð13Þ
kobs
k1KOHK½ATFŠ
k1K½ATFŠ k1
According to Eqs. 12 and 13, plots of 1/kobs versus 1/[ATF] at constant [H?], and 1/kobs
versus [H?] at constant [ATF] should be linear with positive intercepts and are found to be
so as shown in Figs. 8 and 9, respectively. From the slopes and intercepts of these plots the
obtained values of k1, KOH, and K are 13.11 9 10-3 s-1, 0.27 molÁdm-3, and
854.69 dm3Ámol-1, respectively, at 293.2 K.
4.2.2 Reaction Mechanism in Sulfuric Acid Medium
K4
HCe(SO4ÞÀ3 þ HSOÀ4 þ Hþ ꢀ H3CeðSO4ÞÀ4
ð14Þ
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N
N
N
N
H
H
K5
–
+ HCe(SO4)3
(C2)
(15)
(16)
(17)
(18)
(19)
NMe2
NMe2
N
H
N
N
N
H
–
HCe(SO4)3
N
N
N
N
H
.
k2
slow
–
+ Ce3+ + 2SO42– + HSO4 + H+
NMe2
N
H
N
NMe2
N
N
H
–
HCe(SO4)3
N
N
N
N
OH
2–
+ Ce3+ + 2SO4
fast
.
–
+ HCe(SO4)3 + H2O
–
+ HSO4 + H+
NMe2
N
NMe2
N
H
N
N
N
H
N
N
OH
N
N
OH
fast
+
H2O
+
NMe2
fast
N
H
N
H
NH2
O
NMe2
OH
CO2
+
HNMe2
O
NMe2
Scheme 4 Mechanism of oxidation of ATF by Ce(IV) in sulfuric acid solution
The suggested mechanism leads to the following rate law (see Appendix 2):
k2K5½CeðIVފ½ATFŠ
Rate ¼
ð20Þ
1 þ K4½HSOÀ4 Š½HþŠ þ K5½ATFŠ
Under pseudo-first order condition, the rate-law can be expressed by Eq. 21:
Àd½CeðIVފ
Rate ¼
¼ kobs½Ce(IV)Š
ð21Þ
ð22Þ
dt
Comparing Eqs. 20 and 21, the following relationship is obtained,
k2K5½ATFŠ
kobs
¼
1 þ K4½HSOÀ4 Š½HþŠ þ K5½ATFŠ
The rate law (Eq. 22) is consistent with all the observed orders with respect to different
species, which can be verified by rearranging to Eqs. 23 and 24:
ꢀ
ꢁ
1
1 þ K4½HSOÀ4 Š½HþŠ
1
1
¼
þ
ð23Þ
kobs
k2K5
½ATFŠ k2
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J Solution Chem
ꢀ
ꢁ
1
K4
1
1
¼
½HSOÀ4 Š½HþŠ þ
þ
ð24Þ
kobs
k2K5
k2K5½ATFŠ k2
Thus, the plots of 1/kobs versus 1/[ATF] at constant [H?], and 1/kobs versus [H?] at constant
[ATF] should be linear with positive intercepts and are found to be so as shown also in
Figs. 8 and 9, respectively. From the slopes and intercepts of these plots the obtained
values of k2, K4, and K5 are 3.09 9 10-3 s-1, 563.88 dm6Ámol-2, and 336.01 dm3Ámol-1
,
respectively, at 293.2 K.
The obtained activation parameters listed in Table 2 can be discussed as follows. The
negative values of DS suggest interaction of reacting ions of similar charges to form
intermediate complexes of inner-sphere nature [34, 35]. These values are within the range
of radical reactions and have been ascribed to the nature of the electron pairing and
unpairing process and to the loss of degree of freedom formerly available to the reactants
upon formation of a rigid transition state [36, 37]. The values of DH= and DS= are both
favorable for electron transfer processes. On the other hand, the positive values of both
DH= and DG= indicate endothermic formation of the complexes.
The enhancement of oxidation rate upon addition of the metal cations Mn2? and
Al3? can be interpreted by one of several paths, such as formation of complexes with
the reactants, oxidation of the substrate itself or through the formation of free radicals
[38–40].
5 Conclusion
A comparative study of oxidation of one of aminotriazole formamidine derivatives, namely
N,N-dimethyl-N0-(4H-1,2,4-triazol-3-yl) formamidine by cerium(IV) in aqueous perchloric
and sulfuric acid solutions was performed. The rate of oxidation in perchloric acid solution
is about sixfold faster than that observed in sulfuric acid solution. Under our experimental
conditions, Ce(OH)3? and HCe(SO4)3- may be regarded as the active forms of cerium(IV)
in perchloric and sulfuric acid solutions, respectively.
Appendix 1
Derivation of rate law in the case of perchloric acid.
According to the suggested mechanism and regarding to reaction (5),
Àd½CeðIVފ
Rate ¼
Regarding to reactions (3) and (4),
¼ k1½C1Š
ð25Þ
ð26Þ
dt
3þ
½CeðOHÞ Š½HþŠ
KOH½Ce4þ
½HþŠ
Š
3þ
KOH
¼
;
½CeðOHÞ Š ¼
½Ce4þ
Š
and
½C1Š
KOHK½Ce4þŠ½ATFŠ
½HþŠ
K ¼
;
½C1Š ¼ K½Ce(OH)3þŠ½ATFŠ ¼
ð27Þ
3þ
½CeðOHÞ Š½ATFŠ
Substituting Eq. 27 into Eq. 25 leads to,
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J Solution Chem
k1KOHK½Ce4þŠ½ATFŠ
½HþŠ
Rate ¼
ð28Þ
ð29Þ
The total concentration of ATF is given by:
½ATFŠ ¼ ½ATFŠF þ ½C1Š
T
where ‘T’ and ‘F’ stand for total and free concentrations.
Substituting Eq. 27 into Eq. 29 and rearrangement gives,
KOHK½Ce4þŠ½ATFŠ
½ATFŠ ¼ ½ATFŠF þ
ð30Þ
ð31Þ
T
½HþŠ
ꢀ
ꢁ
KOHK½Ce4þ
Š
½ATFŠ ¼ ½ATFŠ 1 þ
T
F
½HþŠ
Therefore,
½ATFŠ
½ATFŠ ¼
ð32Þ
KOHK½Ce4þ
Š
F
1 þ
½HþŠ
In view of low [Ce4?], the second denominator term KOHK[Ce4?]/[H?] in the above
equation is neglected. Therefore,
½ATFŠ ¼ ½ATFŠ
ð33Þ
ð34Þ
F
T
Also,
3þ
½CeðIVފ ¼ ½Ce4þŠF þ ½CeðOHÞ Š þ ½C1Š
T
Substituting Eqs. 26 and 27 into Eq. 34,
KOH½Ce4þ
Š
KOHK½Ce4þŠ½ATFŠ
½CeðIVފ ¼ ½Ce4þŠF þ
þ
ð35Þ
ð36Þ
ð37Þ
T
½HþŠ
½HþŠ
ꢀ
ꢁ
KOH KOHK½ATFŠ
½Ce(IV)Š ¼ ½Ce4þ
Š
1 þ
þ
T
F
½HþŠ
½HþŠ
½CeðIVފ
½HþŠ
½Ce4þŠ ¼
T
F
KOHK½ATFŠ
þ
½HþŠ
KOH
1 þ
Substituting Eqs. 33 and 37 into Eq. 28 (and omitting ‘T’ and ‘F’ subscripts) leads to,
k1KOHK½CeðIVފ½ATFŠ
k1KOHK½CeðIVފ½ATFŠ
Rate ¼
¼
ð38Þ
½HþŠ þ KOH þ KOHK½ATFŠ
KOHK½ATFŠ
KOH
1 þ
þ
½HþŠ
½HþŠ
Under pseudo-first order condition, the rate-law can be expressed by Eq. 39,
Àd½CeðIVފ
Rate ¼
¼ kobs½Ce(IV)Š
ð39Þ
dt
Comparing Eqs. 38 and 39, the following relationship is obtained,
123

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k1KOHK½ATFŠ
kobs
¼
ð40Þ
½HþŠ þ KOH þ KOHK½ATFŠ
and with rearrangement, the following equations are obtained,
ꢀ
ꢁ
1
½HþŠ þ KOH
k1KOHK1
ꢁ
1
1
¼
þ
ð41Þ
ð42Þ
kobs
½ATFŠ k1
ꢀ
1
1
1
1
¼
½HþŠ þ
þ
:
kobs
k1KOHK1½ATFŠ
k1K1½ATFŠ k1
Appendix 2
Derivation of rate law in case of sulfuric acid.
According to the suggested mechanism and regarding to reaction (16),
Àd½CeðIVފ
Rate ¼
Regarding reactions (14) and (15),
¼ k2½C2Š
ð43Þ
dt
½H3CeðSO4ÞÀŠ
½H3CeðSO4ÞÀŠ ¼ K4½HCe(SO4ÞÀŠ½HSOÀŠ½HþŠ ð44Þ
4
K4 ¼
;
½HCeðSO4ÞÀ3 Š½HSOÀ4 Š½HþŠ
4
3
4
½C2Š
K5 ¼
;
½C2Š ¼ K5½HCeðSO4ÞÀŠ½ATFŠ
ð45Þ
½HCeðSO4ÞÀŠ½ATFŠ
Substituting Eq. 45 into Eq. 43 leads to,
3
3
Rate ¼ k2K5½HCeðSO4ÞÀŠ½ATFŠ
The total concentration of ATF is given by:
ð46Þ
ð47Þ
3
½ATFŠ ¼ ½ATFŠF þ ½C2Š
Substituting Eq. 45 into Eq. 47 and rearrangement gives,
T
½ATFŠ ¼ ½ATFŠ þ K5½HCeðSO4ÞÀŠ½ATFŠ
ð48Þ
ð49Þ
T
F
3
½ATFŠ ¼ ½ATFŠ ð1 þ K5½HCeðSO4ÞÀŠÞ
F
3
Therefore,
½ATFŠ
T
½ATFŠ ¼
ð50Þ
1 þ K5½HCeðSO4ÞÀŠ
F
3
In view of low [HCe(SO4)-3 ], the second numerator term in the above equation is
neglected. Therefore,
½ATFŠ ¼ ½ATFŠ
ð51Þ
F
T
Also,
123

J Solution Chem
½CeðIVފ ¼ ½HCeðSO4ÞÀŠ þ ½H3CeðSO4ÞÀŠ þ ½C2Š
ð52Þ
T
3
4
Substituting Eqs. 44 and 45 into Eq. 52,
½CeðIVފ ¼ ½HCe(SO4ÞÀŠ þ K4½HCe(SO4ÞÀŠ½HSOÀŠ½HþŠ þ K5½HCe(SO4ÞÀŠ½ATFŠ ð53Þ
T
3
3
4
3
½CeðIVފ ¼ ½HCe(SO4ÞÀŠð1 þ K4½HSOÀŠ½HþŠ þ K5½ATFŠÞ
ð54Þ
T
3
4
½CeðIVފ
½HCeðSO4ÞÀŠ ¼
ð55Þ
T
3
1 þ K4½HSOÀ4 Š½HþŠ þ K5½ATFŠ
Substituting Eqs. 51 and 55 into Eq. 46 leads to,
k2K5½CeðIVފ½ATFŠ
Rate ¼
ð56Þ
1 þ K4½HSOÀ4 Š½HþŠ þ K5½ATFŠ
Under pseudo-first order condition, the rate-law can be expressed by Eq. 57,
Àd½CeðIVފ
Rate ¼
¼ kobs½CeðIVފ
ð57Þ
ð58Þ
dt
Comparing Eqs. 56 and 57, the following relationship is obtained,
k2K5½ATFŠ
kobs
¼
1 þ K4½HSOÀ4 Š½HþŠ þ K5½ATFŠ
and with rearrangement, the following equations are obtained:
ꢀ
ꢁ
1
1 þ K4½HSOÀ4 Š½HþŠ
1
1
¼
þ
ð59Þ
ð60Þ
kobs
k2K5
½ATFŠ k2
ꢀ
ꢁ
1
K4
k2K5
1
1
¼
½HSOÀ4 Š½HþŠ þ
þ
:
kobs
k2K5½ATFŠ k2
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123